## Comparison of discrete ordinate and Monte Carlo simulations of polarized radiative transfer in two coupled slabs with different refractive indices |

Optics Express, Vol. 21, Issue 8, pp. 9592-9614 (2013)

http://dx.doi.org/10.1364/OE.21.009592

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### Abstract

A comparison is presented of two different methods for polarized radiative transfer in coupled media consisting of two adjacent slabs with different refractive indices, each slab being a stratified medium with no change in optical properties except in the direction of stratification. One of the methods is based on solving the integro-differential radiative transfer equation for the two coupled slabs using the discrete ordinate approximation. The other method is based on probabilistic and statistical concepts and simulates the propagation of polarized light using the Monte Carlo approach. The emphasis is on non-Rayleigh scattering for particles in the Mie regime. Comparisons with benchmark results available for a slab with constant refractive index show that both methods reproduce these benchmark results when the refractive index is set to be the same in the two slabs. Computed results for test cases with coupling (different refractive indices in the two slabs) show that the two methods produce essentially identical results for identical input in terms of absorption and scattering coefficients and scattering phase matrices.

© 2013 OSA

**OCIS Codes**

(010.0010) Atmospheric and oceanic optics : Atmospheric and oceanic optics

(010.1290) Atmospheric and oceanic optics : Atmospheric optics

(010.4450) Atmospheric and oceanic optics : Oceanic optics

(280.0280) Remote sensing and sensors : Remote sensing and sensors

(010.5620) Atmospheric and oceanic optics : Radiative transfer

**ToC Category:**

Atmospheric and Oceanic Optics

**History**

Original Manuscript: January 24, 2013

Revised Manuscript: March 14, 2013

Manuscript Accepted: March 15, 2013

Published: April 10, 2013

**Virtual Issues**

Vol. 8, Iss. 5 *Virtual Journal for Biomedical Optics*

**Citation**

D. Cohen, S. Stamnes, T. Tanikawa, E. R. Sommersten, J. J. Stamnes, J. K. Lotsberg, and K. Stamnes, "Comparison of discrete ordinate and Monte Carlo simulations of polarized radiative transfer in two coupled slabs with different refractive indices," Opt. Express **21**, 9592-9614 (2013)

http://www.opticsinfobase.org/vjbo/abstract.cfm?URI=oe-21-8-9592

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### References

- H. R. Gordon, “Atmospheric correction of ocean color imagery in the Earth Observation System era,” J. Geophys. Res.102, 17081–17106 (1997). [CrossRef]
- M. Mishchenko and L. Travis, “Satellite retrieval of aerosol properties over the ocean using polarization as well as intensity of reflected sunlight,” J. Geophys. Res.102, 16989–7013 (1997). [CrossRef]
- C. Rodgers, Inverse Methods for Atmospheric Sounding (World Scientific, 2000).
- W. Li, K. Stamnes, R. Spurr, and J. J. Stamnes, “Simultaneous retrieval of aerosols and ocean properties: A classic inverse modeling approach. II. SeaWiFS case study for the Santa Barbara channel,” Int. J. Rem. Sens.29, 5689–5698 (2008). [CrossRef]
- Z. Jin and K. Stamnes, “Radiative transfer in nonuniformly refracting layered media: atmosphere-ocean system,” Appl. Opt.33, 431–442 (1994). [CrossRef] [PubMed]
- R. Spurr, K. Stamnes, H. Eide, W. Li, K. Zhang, and J. J. Stamnes, “Simultaneous retrieval of aerosol and ocean properties: A classic inverse modeling approach: I. Analytic Jacobians from the linearized CAO-DISORT model,” J. Quant. Spectrosc. Radiat. Transfer104, 428–449 (2007). [CrossRef]
- K. Nielsen, L. Zhao, G. A. Ryzhikov, M. S. Biryulina, E. R. Sommersten, J. J. Stamnes, K. Stamnes, and J. Moan, “Retrieval of the physiological state of human skin from UV-VIS reflectance spectra: A feasibility study,” J. Photochem. Photobiol. B93, 23–31 (2008). [CrossRef] [PubMed]
- D. L. Swanson, S. D. Laman, M. Biryulina, K. P. Nielsen, G. Ryzhikov, J. J. Stamnes, B. Hamre, L. Zhao, F. S. Castellana, and K. Stamnes, “Optical transfer diagnosis of pigmented lesions: a pilot study,” Skin Res. Technol.15, 330–337 (2009). [CrossRef] [PubMed]
- D. L. Swanson, S. D. Laman, M. Biryulina, K. P. Nielsen, G. Ryzhikov, J. J. Stamnes, B. Hamre, L. Zhao, E. Sommersten, F. S. Castellana, and K. Stamnes, “Optical transfer diagnosis of pigmented lesions,” Dermatol. Surg.36, 1–8 (2010). [CrossRef]
- C. N. Adams and G. W. Kattawar, “Stokes vector calculations of the submarine light field in an atmosphere-ocean with scattering according to a Rayleigh phase matrix: Effect of interface refractive index on radiance and polarization,” Limm. Ocean.34, 1453–1472 (1989). [CrossRef]
- M. I. Mishchenko, A.A. Lacis, and L. D. Travis, “Errors due to the neglect of polarization in radiance calculations for Rayleigh-scattering atmospheres,” J. Quant Spectrosc. Radiat Transfer51, 491–510 (1994). [CrossRef]
- A. A. Lacis, J. Chowdhary, M. I. Mishchenko, and B. Cairns, “Modeling errors in diffuse-sky radiation: vector vs. scalar treatment,” Geophys. Res. Lett.25, 135–138 (1998). [CrossRef]
- S. Chandrasekhar, Radiative Transfer (Dover Publications, 1960).
- K. N. Liou, “A numerical experiment on Chandrasekhar’s discrete-ordinate method for radiative transfer,” J. Atmos. Sci.30, 1303–1326 (1973). [CrossRef]
- K. Stamnes and R. A. Swanson, “A new look at the discrete ordinate method for radiative transfer calculations in anisotropically scattering atmospheres,” J. Atmos. Sci.38, 387–399 (1981). [CrossRef]
- K. Stamnes and H. Dale, “A new look at the discrete ordinate method for radiative transfer calculations in anisotropically scattering atmospheres. II. Intensity computations,” J. Atmos. Sci.38, 2696–2706 (1981). [CrossRef]
- K. Stamnes and P. Conklin, “A new multi-layer discrete ordinate approach to radiative transfer in vertically inhomogeneous atmospheres,” J. Quant. Spectrosc. Radiat. Transfer31, 273–282 (1984). [CrossRef]
- K. Stamnes, S.-C. Tsay, W. Wiscombe, and K. Jayaweera, “Numerically stable algorithm for discrete-ordinate-method radiative transfer in multiple scattering and emitting layered media,” Appl. Opt.272502–2509 (1988). [CrossRef] [PubMed]
- K. P. Nielsen, L. Zhao, P. Juzenas, K. Stamnes, J. J. Stamnes, and J. Moan, “Reflectance spectra of pigmented and non-pigmented skin in the UV spectral region,” Photochem. Photobiol.80, 450–455 (2004). [PubMed]
- K. I. Gjerstad, J. J. Samnes, B. Hamre, J. K. Lotsberg, B. Yan, and K. Stamnes, “Monte Carlo and discrete-ordinate simulations of irradiances in the coupled atmosphere-ocean system,” Appl. Opt.42, 2609–2622 (2003). [CrossRef] [PubMed]
- K. Hestenes, K. P. Nielsen, L. Zhao, J. J. Stamnes, and K. Stamnes, “Monte Carlo and discrete-ordinate simulations of spectral radiances in the coupled air-tissue system,” Appl. Opt.46, 2333–2350 (2007). [CrossRef] [PubMed]
- F. Weng, “A multi-layer discrete-ordinate method for vector radiative transfer in a vertically-inhomogenous, emitting and scattering atmosphere - I. Theory,” J. Quant. Spectrosc. Radiat. Transfer, 47, 19–33 (1992). [CrossRef]
- F. Weng, “A multi-layer discrete-ordinate method for vector radiative transfer in a vertically-inhomogenous, emitting and scattering atmosphere - II. Applications,” J. Quant. Spectrosc. Radiat. Transfer47, 35–42 (1992). [CrossRef]
- F. M. Schulz, K. Stamnes, and F. Weng, “VDISORT: An improved and generalized discrete ordinate method for polarized vector radiative transfer,” J. Quant. Spectrosc. Radiat. Transfer61, 105–122 (1999). [CrossRef]
- F. M. Schulz and K. Stamnes, “Angular distribution of the Stokes vector in a plane parallel, vertically inhomogeneous medium in the vector discrete ordinate radiative transfer (VDISORT) model,” J. Quant. Spectrosc. Radiat. Transfer65, 609–620 (2000). [CrossRef]
- S. Jiang, “Radiative Transfer in the Coupled Atmosphere-Sea Ice-Ocean System with Applications in Remote Sensing,” PhD thesis, Stevens Institute of Technology (2003).
- E. R. Sommersten, “CAO-VDISORT: A discrete ordinate method for polarized (vector) radiative transfer in a coupled system consisting of two media with different indices of refraction,” MSc thesis, University of Bergen (2005).
- E. R. Sommersten, J. K. Lotsberg, K. Stamnes, and J. J. Stamnes, “Discrete ordinate and Monte Carlo simulations for polarized radiative transfer in a coupled system consisting of two media with different refractive indices,” J. Quant. Spectrosc. Radiat. Transfer111, 616–633 (2010). [CrossRef]
- W. J. Wiscombe, “The delta-M method: Rapid yet accurate radiative flux calculations for strongly asymmetric phase functions,” J. Atmos. Sci.34, 1408–1422 (1977). [CrossRef]
- J. K. Lotsberg, “Impact of particulate oceanic composition on the radiance and polarization of the natural light field,” PhD thesis, University of Bergen (2005).
- J. K. Lotsberg and J. J. Stamnes, “Impact of particulate oceanic composition on the radiance and polarization of underwater and backscattered light,” Opt. Expr.18, 10432–10445 (2010). [CrossRef]
- G. N. Plass and G. W. Kattawar, “Monte Carlo calculations of light scattering from clouds,” Appl. Opt.7, 415–419 (1968). [CrossRef] [PubMed]
- G. I. Marchuk, G. A Mikhailov, M. A. Nazaraliev, R. A. Darbinjan, B. A. Kargin, and B. S. Elepov, The Monte Carlo Methods in Atmospheric Optics (Springer-Verlag, 1980). [CrossRef]
- H. H. Tynes, G. W. Kattawar, E. P. Zege, I. L. Katsev, A. S. Prikhach, and L. I. Chaikovskaya, “Monte Carlo and multicomponent approximation methods for vector radiative transfer by use of effective Mueller matrix calculations,” Appl. Opt.40, 400–412 (2001). [CrossRef]
- H. Ishimoto and K. Masuda, “A Monte Carlo approach for the calculation of polarized light,” J. Quant. Spectrosc. Radiat. Transfer72, 467–483 (2002). [CrossRef]
- D. M. O’Brien, “Accelerated quasi Monte Carlo integration of the radiative transfer equation,” J. Quant. Spectrosc. Radiat. Transfer48, 41–59 (1992). [CrossRef]
- P. W. Zhai, Y. Hu, J. Chowdhary, C. R. Trepte, P. L. Lucker, and D. B. Josset, “A vector radiative transfer model for coupled atmosphere and ocean systems based on successive order of scattering method,” Opt. Expr.17, 2057–2079 (2009). [CrossRef]
- C. E. Siewert, “On the equation of transfer relevant to the scattering of polarized light,” Astrophys. J.245, 1080–1086 (1981). [CrossRef]
- C. E. Siewert, “On the phase matrix basic to the scattering of polarized light,” Astron. Astrophys.109, 195–200 (1982).
- J. F. de Haan, P. B. Bosma, and J. W. Hovenier, “The adding method for multiple scattering calculations of polarized light,” Astron. Astrophys.183, 371–391 (1987).
- J. M. Wallace and P. V. Hobbs, Atmospheric Science: Introductory Survey (Academic, 1977).
- C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (John Wiley, 1998). [CrossRef]
- X. Zhou, S. Li, and K. Stamnes, “Geometrical-optics code for computing optical properties of large dielectric spheres,” Appl. Opt.42, 4295–4306 (2003). [CrossRef] [PubMed]
- J. E. Hansen and L. D. Travis, “Light scattering in planetary atmospheres,” Space Sci. Rev.16, 527–610 (1974). [CrossRef]
- A. A. Kokhanovsky, C. Cornet, M. Duan, C. Emde, I. L. Katsev, L. C-Labonnote, Q. Min, T. Nakajima, Y. Ota, and A.P. Prikhach, and others, “Benchmark results in vector radiative transfer,” J. Quant. Spectrosc. Radiat. Transfer111, 1931–1946 (2010). . [CrossRef]
- M. I. Mishchenko, “Light scattering by randomly oriented rotationally symmetric particles,” J. Opt. Soc. Am. A8, 871–882 (1991). [CrossRef]
- M. I. Mischenko and L. D. Travis, “Capabilities and Limitations of a Current FORTRAN Implementation of the T-Matrix Method for Randomly Oriented, Rotationally Symmetric Scatterers,” J. Quant. Spectrosc. Radiat. Transfer60, 309–324 (1998). [CrossRef]
- M. I. Mishchenko, L. D. Travis, and A. A. Lacis, Scattering, Absorption, and Emission of Light by Small Particles (Cambridge University, 2002).
- M. Born and E. Wolf, Principles of Optics: 7th edition (Cambridge University, 2002).
- J. F. de Haan, P. B. Bosma, and J. W. Hovenier, “The adding method for multiple scattering calculations of polarized light,” Astron. Astrophys.183, 371–391 (1987).
- J. W. Hovenier and C. V. M. van der Mee, “Fundamental relationships relevant to the transfer of polarized light in a scattering atmosphere,” Astron. Astrophys.128, 1–16 (1983).

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